Values of the Gas Constant in Different Unit

The value of R changes if we express the ideal-gas equation (Equation (1.13)) with different units. Table 2.3 gives values of R in various other units. We must note an important philosophical truth here the value of the gas constant is truly constant, but the actual numerical value we cite will depend on the units with which we express it. We met a similar argument before on p. 19, when we saw how a standard prefix (such as deca, milli or mega) will change the appearance of a number, so V = 1 dm3 = 103 cm3. In reality, the number remains unaltered. 

The quantities 8.314 X 10 and 0.08314 are values of the gas constant expressed in different units (see inside back cover). 

The ideal gas equation combines the variables of temperature, pressure and volume that we have been dealing with in the previous sections, but also allows us to calculate the mass in either grammes or moles and also an approximate molar mass for the particular gas. The previous gas laws involved an unknown constant that we eliminated from the calculation by taking temperatures, etc, at two different levels. In the ideal gas equation, we are introduced to the universal gas constant, R, which enables us to do the measurements under one set of conditions only. The difficulty arising from this is that the units of the gas constant are dependent on the units in which the other variables are measured, so it is important to think about the units you are working in. A selection of values for R using different units is listed in Table 4.5.3. 

The exponential dependence of the strain rate on the temperature has been confirmed experimentally. The relation between strain rate and stress is found to follow a power law, as predicted by the equation (see also section 11.1), but in reality the creep exponent typically takes values between 3 and 8. Due to the large variations of the creep exponent in different materials, the value of the factor A can differ by several orders of magnitude. The activation energy in equation (11.13) is frequently stated per mole in the units kJ/mol. In this case, Boltzmann s constant k has to be replaced by the gas constant R in the equation as explained in appendix C.l. 

The proportionality constant, R, in Equation 11.6 is called thegas constant. Its value and units depend on the units in which P and V are expressed. (The variables n and T are always expressed in mol and K, respectively.) Recall from Section 11.1 that pressure is commonly expressed in atmospheres, mmHg (ttjrr), pascals, or bar. Volume is typically expressed in liters or milliliters, but can also be expressed in other units, such as m. Table 11.4 lists several different expressions of the gas constant. R. 

Based on the values in the formula the least number of significant figures is five so we need to round off R to five significant figures as 0.082057 (L atm/°K mol). We note that 22.414 L is about the size of a 5 gal solvent can and we need to tabulate some key unit facts in this first chapter. At this point it is easy to introduce the SI equivalent of the gas constant since the only difference is that the pressure is measured in bars where 1 atm= 1.01325 bar. (Note that a barometer measures bars.) However, at the lower pressure the molar volume will be larger at about 22.711 L ... 

As indicated in Eq. (27.13), the specific heat capacity depends unambiguously on 0D and hence on the size, temperature, and the bond nature involved. Figure 27.6a shows the reduced Cy (in units of the gas constant R) versus temperature (TIBdo) for Si nanowires (m = 4.88) and A1 nanowires (m = 1) of different diameters (A = 5, 10, and 20). The shape of the Cy curve is similar to that of the bulk but the size induces a depression over the whole temperature range. For the same A at a given Tl9 o, the reduction in heat capacity increases with the m value. 

FIGURE 19 (a) The entropy Sof liquid and solid He (upper diagram) measured in units of the gas constant R, plotted as functions of temperature T and the melting pressure Pm of He as a function of T. It may be noted that the minimum in the melting curve occurs at the temperature where the difference between the solid and liquid entropies changes sign. [From values tabulated by Betts, D. S. (1976). Refrigeration and Thermometry Below One Kelvin, Sussex Univ. Press, London.]... 

Values for the gas constant, R, in different units are given in Table 1.1. The ideal gas model was empirically developed largely through the work of the chemists Boyle, Gay-Lussac, and Charles. It is valid for gases in the limits of low pressure and high temperature. In practice, the behavior of most gases at atmospheric pressure is well approximated... 

At integrating (305) for the conditions of a flow system (93, 98), it proved to be convenient to introduce a constant k proportional to k. The value of k was also calculated from data obtained in circulation flow systems (4, 96, 99-103). If the volume of ammonia reduced to 0°C and 1 atm, formed in unit volume of catalyst bed per hour, is accepted as a measure of reaction rate, then k = (4/3)3 1 m)k (101). The constancy of k at different times of contact of the gas mixture with the catalyst and different N2/H2 ratios in the gas mixture can serve as a criterion of applicability of (305). Such constancy was obtained for an iron catalyst of a commercial type promoted with A1203 and K20 at m = 0.5 (93) from our own measurements at atmospheric pressure in a flow system and literature data on ammonia synthesis at elevated pressures up to 100 atm. A more thorough test of applicability of (305) to the reaction on a commercial catalyst at high pressures was done by means of circulation flow method (99), it confirmed (305) with m = 0.5 for pressures up to 300 atm. Similar results were obtained in a large number of investigations by different authors in the USSR and abroad. These authors, however, have obtained for some promoted iron catalysts m values differing from 0.5. Thus, Nielsen et al. (104) have found that m 0.7. 

For miscible blend phases, these parameters need to be described as a function of the blend composition. In a first approach to describe the behavior of the present PPE/PS and SAN/PMMA phases, these phases will be regarded as ideal, homogeneously mixed blends. It appears reasonable to assume that the heat capacity, the molar mass of the repeat unit, as well as the weight content of carbon dioxide scale linearly with the weight content of the respective blend phase. Moreover, a constant value of the lattice coordination number for PPE/PS and for SAN/PMMA can be anticipated. Thus, the glass transition temperature of the gas-saturated PPE/SAN/SBM blend can be predicted as a function of the blend composition (Fig. 17). Obviously, both the compatibilization by SBM triblock terpolymers and the plasticizing effect of the absorbed carbon dioxide help to reduce the difference in glass transition temperature between PPE and SAN. 

Here, Epro is the energy for the production of a certain amount of acid and base, I is the current passing through the stack, Nceu is the number of cell units in a stack, A n is the cell unit area, C and C are the concentration and the average concentration in a cell, A is the thickness of the individual cells, and A is the equivalent conductivity, r is the area resistance, , is the current utilization, R is the gas constant, T the absolute temperature, F the Faraday constant, and ApH is the difference in the pH value between the acid and base, the subscript p refers to product and the subscript i refers to salt, acid and base, The superscripts am, cm, and bm refer to the cation-exchange, the anion-exchange, and the bipolar membrane, the superscript out and in refer to cell outlet and inlet, Q is the total flow of the acid or base through the stack and t is the time. 

C = coefficient of heat conductivity measured in heat units per unit time per unit of packing volume per deg temperature difference usual units are cal per sec per deg C per cc m = a constant for limestone packings, m = 0.0073 for iron ore, 0.0105 anthracite and other coals, 0.0050 blast-furnace charge, 0.0072. The values are in metric units. q = volume of gas flow per unit-time per square unit of cross-sectional packing area, expressed as liters per sec per sq cm T = temperature, deg abs, C = fractional voids (dimensionless) d = diameter of particles, cm... 

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